No. There is no need to complete an assessment on Higg if you have a BW assessment.
If your BW profile is connected to the Gateway, your BW assessment data is automatically shared with the Gateway. In your Gateway profile, you can find your BW assessment data and send it to Higg.
Choose to "share with another accredited host" under the menu item "Overview of my SLCP assessment". More guidance is in this FAQ.
Higg can use your BW assessment data to complete your vFSLM and provide you with an FSLM score. Find guidance on how to share data from BW to Higg here.
As BW and SLCP use the same Data Collection Tool, your BW assessment data is exactly the same as SLCP-verified data.
Note: your buyers may need Step 2 or 3 data. BW only assesses Step 1. If you need Step 2 or 3 data, you need to complete Step 2 or 3 in your self-assessment.
More guidance on how to connect your BW profile to the Gateway and start your assessment here.